Echoes are common in many areas of physics, including NMR, plasma physics, nonlinear optics, cavity quantum electrodynamics, cold atoms physics, and dynamics of proton storage rings. Recently we found (probably) the simplest system featuring the echo phenomenon—a collection of randomly oriented free rotors with dispersed rotational velocities. Following excitation by a pair of time delayed impulsive kicks, the mean orientation or alignment of the ensemble is predicted to exhibit multiple echoes and fractional echoes. We elucidate the mechanism of the echo formation by the kick-induced filamentation of the rotational phase space, and provide the first experimental demonstration of alignment echoes by measuring laser-induced birefringence in a thermal gas of CO2 molecules excited by a pair of femtosecond laser pulses [1]. Fractional echoes in the same system were detected via the third harmonic generation from an additional probe pulse [2]. More recently, we used the technique of coincidence Coulomb explosion imaging for a direct spatiotemporal analysis of various molecular alignment echoes [3] and observed fractional echoes of high order, spatially rotated echoes, and counter-intuitive imaginary echoes at negative times. The described mechanism of the echo formation is rather general and has implications in other fields of physics. The recent SLAC demonstration of the efficient generation of high harmonics (up to the 75th) from tailored electron beams in free-electron lasers [4] is based on a mechanism similar to fractional echoes of high order observed in our molecular experiments.